With the incoming Congress looking for accomplishments, here’s one the Republican majority should take up immediately: immigration reform. Contrary to conventional wisdom, Republicans are its natural champions. The GOP led the way in 1986 and 1996, when partial immigration reforms were enacted. And a Republican Senate, with the support of President George W. Bush, passed comprehensive reform in 2006, only to see it die in the House.

Under President Barack Obama and a House run by Nancy Pelosi, immigration became a wedge used to separate Hispanic voters from the Republican Party. Thus came the sad spectacle of the Justice Department suing to block Arizona’s common-sense enforcement efforts. Congress’s failure to move any legislation on the issue has only added to the public’s discontent.

Republicans should break this logjam by offering a vision of sensible immigration reform that can benefit U.S. citizens and boost America’s influence globally. Such reform should focus on three critical national interests: security, the economy and freedom.

Security is first: Immigration must be viewed in a post-9/11 context. Immigration enforcement—including background checks for visa issuance, customs and border security, and apprehension of dangerous illegal aliens—is the frontline in the campaign against terrorism. Unfortunately, Congressional Democrats resisted even minor reforms.

For example, if the State Department receives intelligence that a person visiting the U.S. poses a security threat, his visa can be revoked. But visa revocation does not automatically extinguish a person’s right to remain in the U.S., even though he couldn’t re-enter legally. This—and similar loopholes—must be corrected right away.

The border fence is another area where Democrats have refused to make security a priority. A Republican Congress passed the Secure Fence Act in 2006 by veto-proof majorities. This law required surveillance and the prevention of unlawful entry into the U.S., naming high-risk areas along the Mexican border for extra attention.

The fence is now over two years past due. Meanwhile, mountains of illicit drugs—including 90% of cocaine in this country—are trafficked through Mexico. Many legal aliens are coerced by drug traffickers to participate in their operations, so trafficking in persons (labor- related and sex- related) is also on the rise.

But our security interests are tied to our economic interests. Blocking all opportunities for Mexican workers to enter the U.S. job market would exacerbate that country’s already grave political, security and economic problems. Most illegal aliens cross the border for work; even in the current economy many come because the jobs are here.

Few U.S. workers seek employment as seasonal or agricultural laborers, or clamor for other physically taxing jobs. The construction trades—historically passed along from generation to generation—are now dominated by foreign workers (legal and illegal). For those jobs, Congress must sweep away current regulations requiring employers to house and transport foreign laborers, eliminate burdensome paperwork, and generally refashion a guest-worker program into a user-friendly and attractive economic option.

Reform is also needed at the high-skill end of the job market. Today, we spend taxpayer dollars educating brilliant foreign students in math and science at U.S. universities—and then deny them visas to work here. Meanwhile, we blame U.S. businesses for moving operations overseas in search of workers with doctorates. In the global competition for talent, Congress must ensure that U.S. businesses have access to the most talented workers by increasing the current visa caps. A guest-worker program and more visas for skilled workers would regulate the flow of aliens into the U.S., allowing border agents to focus on real threats.

For years, Congress has struggled mightily for a solution to the estimated 12 million-plus illegal aliens already in the country. This is the most difficult and politically contentious piece of immigration reform. A legalization-only approach—even if targeted at a subset of the illegal alien population, as the Dream Act is for college-bound students—would only ensure that, several years from now, there would be millions more new illegal aliens attracted by the hope of future legalization. Across-the-board legalization, particularly if it involves an automatic path towards citizenship, would reward decades’ worth of lawbreaking.

The best approach is a gradual and targeted legalization program that serves our economic needs. For skilled workers, employers should be in the driver’s seat to identify who is most needed for economic growth. For low-skill jobs that few or no Americans are willing to perform, Congress should enact a robust temporary guest-worker program—and U.S. employers must accept mandatory electronic verification for foreign workers based on tamper-proof identification.

Along with our security and economic interests, immigration should reflect our fundamental commitment to liberty. If a U.S. citizen chooses to marry a foreigner, for instance, she shouldn’t be put through the bureaucratic grinder to obtain legal status for her spouse. The U.S. has traditionally provided refuge for those suffering oppression and human-rights abuses, and we should continue to do so. Congress should also encourage the safe return of refugees and asylum-seekers as future reformers when conditions in their home countries ease.

Immigration is closely tied to everything that makes America great—our might, our wealth and our freedom. Because Democrats have ignored that fact, the door is wide open for Republicans to come through and deliver.

Mr. Jacquot is the deputy attorney general of Florida and the former chief counsel for the U.S. Senate’s Immigration Subcommittee. Mr. Rivkin is a Washington-based lawyer and served in the Department of Justice under Presidents Reagan and George H.W. Bush.